Changes

: Relativity does imply that space as well as space-time are curved.  The observation of a flat universe does contradict what would be expected if Relativity were true.--[[User:Aschlafly|Andy Schlafly]] 10:03, 13 August 2010 (EDT)

: Relativity does imply that space as well as space-time are curved.  The observation of a flat universe does contradict what would be expected if Relativity were true.--[[User:Aschlafly|Andy Schlafly]] 10:03, 13 August 2010 (EDT)

:: :: A trivial solution to Einsteins field equations for a vacuum can result in Minkowski spacetime. This is a 4D metric describing a pseudo-Riemannian manifold with no spatial curvature (i.e. flat). A requirement of GR is that in locally inertial frames (i.e. small enough regions of spacetime) we recover Minkowski spacetime. It's just that in GR the requirement of a locally Minkwoski spacetime does not always extend to a global case with curvature effects breaking down the notion of inertial frames for all observers. The observation of a flat Universe (spatial curvature parameter, K = 0 in the FLRW metric) is not in violation of GR and is a valid solution to Einsteins field equations (see e.g. Friedmanns Equations) and a prediction of models of inflationary cosmology whereby a rapid expansion in the early Universe drives the Universe towards a spatially flat solution, certainly within the observable Universe. Predictions from GR are still obeyed contrary to the comment "flat universe does contradict what would be expected if Relativity were true". The observed flatness of the Universe is commonly attributed to a period of rapid expansion (e.g. Inflationary Cosmology) in which the expansion drives the observable Universe to a spatially flat solution in the FLRW models of the Universe. Essentially the observed spatial flatness of the Universe is in no way contradictory to predictions of GR and a spatially flat Universe is a generic prediction from models for inflation. I do not feel that the point in discussion is in any way a counterpoint to relativity. If other objections arise then perhaps this point would need to be further clarified so that any issues may be appropriately discussed? 15th August 2010

:::: A trivial solution to Einsteins field equations for a vacuum can result in Minkowski spacetime. This is a 4D metric describing a pseudo-Riemannian manifold with no spatial curvature (i.e. flat). A requirement of GR is that in locally inertial frames (i.e. small enough regions of spacetime) we recover Minkowski spacetime. It's just that in GR the requirement of a locally Minkwoski spacetime does not always extend to a global case with curvature effects breaking down the notion of inertial frames for all observers. The observation of a flat Universe (spatial curvature parameter, K = 0 in the FLRW metric) is not in violation of GR and is a valid solution to Einsteins field equations (see e.g. Friedmanns Equations) and a prediction of models of inflationary cosmology whereby a rapid expansion in the early Universe drives the Universe towards a spatially flat solution, certainly within the observable Universe. Predictions from GR are still obeyed contrary to the comment "flat universe does contradict what would be expected if Relativity were true".

 

:::: I do not feel that the point in discussion is in any way a counterpoint to relativity. If other objections arise then perhaps this point would need to be further clarified so that any issues may be appropriately discussed? 15th August 2010

== Reversion explained ==

== Reversion explained ==